2x-3(x-6)-1(x-6)(x-6)=x(x-6)

Solution for 2x-3(x-6)-1(x-6)(x-6)=x(x-6) equation:

Simplifying
2x + -3(x + -6) + -1(x + -6)(x + -6) = x(x + -6)

Reorder the terms:
2x + -3(-6 + x) + -1(x + -6)(x + -6) = x(x + -6)
2x + (-6 * -3 + x * -3) + -1(x + -6)(x + -6) = x(x + -6)
2x + (18 + -3x) + -1(x + -6)(x + -6) = x(x + -6)

Reorder the terms:
2x + 18 + -3x + -1(-6 + x)(x + -6) = x(x + -6)

Reorder the terms:
2x + 18 + -3x + -1(-6 + x)(-6 + x) = x(x + -6)

Multiply (-6 + x) * (-6 + x)
2x + 18 + -3x + -1(-6(-6 + x) + x(-6 + x)) = x(x + -6)
2x + 18 + -3x + -1((-6 * -6 + x * -6) + x(-6 + x)) = x(x + -6)
2x + 18 + -3x + -1((36 + -6x) + x(-6 + x)) = x(x + -6)
2x + 18 + -3x + -1(36 + -6x + (-6 * x + x * x)) = x(x + -6)
2x + 18 + -3x + -1(36 + -6x + (-6x + x2)) = x(x + -6)

Combine like terms: -6x + -6x = -12x
2x + 18 + -3x + -1(36 + -12x + x2) = x(x + -6)
2x + 18 + -3x + (36 * -1 + -12x * -1 + x2 * -1) = x(x + -6)
2x + 18 + -3x + (-36 + 12x + -1x2) = x(x + -6)

Reorder the terms:
18 + -36 + 2x + -3x + 12x + -1x2 = x(x + -6)

Combine like terms: 18 + -36 = -18
-18 + 2x + -3x + 12x + -1x2 = x(x + -6)

Combine like terms: 2x + -3x = -1x
-18 + -1x + 12x + -1x2 = x(x + -6)

Combine like terms: -1x + 12x = 11x
-18 + 11x + -1x2 = x(x + -6)

Reorder the terms:
-18 + 11x + -1x2 = x(-6 + x)
-18 + 11x + -1x2 = (-6 * x + x * x)
-18 + 11x + -1x2 = (-6x + x2)

Solving
-18 + 11x + -1x2 = -6x + x2

Solving for variable 'x'.

Reorder the terms:
-18 + 11x + 6x + -1x2 + -1x2 = -6x + x2 + 6x + -1x2

Combine like terms: 11x + 6x = 17x
-18 + 17x + -1x2 + -1x2 = -6x + x2 + 6x + -1x2

Combine like terms: -1x2 + -1x2 = -2x2
-18 + 17x + -2x2 = -6x + x2 + 6x + -1x2

Reorder the terms:
-18 + 17x + -2x2 = -6x + 6x + x2 + -1x2

Combine like terms: -6x + 6x = 0
-18 + 17x + -2x2 = 0 + x2 + -1x2
-18 + 17x + -2x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
-18 + 17x + -2x2 = 0

Begin completing the square.  Divide all terms by
-2 the coefficient of the squared term: 

Divide each side by '-2'.
9 + -8.5x + x2 = 0

Move the constant term to the right:

Add '-9' to each side of the equation.
9 + -8.5x + -9 + x2 = 0 + -9

Reorder the terms:
9 + -9 + -8.5x + x2 = 0 + -9

Combine like terms: 9 + -9 = 0
0 + -8.5x + x2 = 0 + -9
-8.5x + x2 = 0 + -9

Combine like terms: 0 + -9 = -9
-8.5x + x2 = -9

The x term is -8.5x.  Take half its coefficient (-4.25).
Square it (18.0625) and add it to both sides.

Add '18.0625' to each side of the equation.
-8.5x + 18.0625 + x2 = -9 + 18.0625

Reorder the terms:
18.0625 + -8.5x + x2 = -9 + 18.0625

Combine like terms: -9 + 18.0625 = 9.0625
18.0625 + -8.5x + x2 = 9.0625

Factor a perfect square on the left side:
(x + -4.25)(x + -4.25) = 9.0625

Calculate the square root of the right side: 3.010398645

Break this problem into two subproblems by setting 
(x + -4.25) equal to 3.010398645 and -3.010398645.

Subproblem 1
x + -4.25 = 3.010398645

Simplifying
x + -4.25 = 3.010398645

Reorder the terms:
-4.25 + x = 3.010398645

Solving
-4.25 + x = 3.010398645

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '4.25' to each side of the equation.
-4.25 + 4.25 + x = 3.010398645 + 4.25

Combine like terms: -4.25 + 4.25 = 0.00
0.00 + x = 3.010398645 + 4.25
x = 3.010398645 + 4.25

Combine like terms: 3.010398645 + 4.25 = 7.260398645
x = 7.260398645

Simplifying
x = 7.260398645

Subproblem 2
x + -4.25 = -3.010398645

Simplifying
x + -4.25 = -3.010398645

Reorder the terms:
-4.25 + x = -3.010398645

Solving
-4.25 + x = -3.010398645

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '4.25' to each side of the equation.
-4.25 + 4.25 + x = -3.010398645 + 4.25

Combine like terms: -4.25 + 4.25 = 0.00
0.00 + x = -3.010398645 + 4.25
x = -3.010398645 + 4.25

Combine like terms: -3.010398645 + 4.25 = 1.239601355
x = 1.239601355

Simplifying
x = 1.239601355

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {7.260398645, 1.239601355}